yield income question

CFA Level III
#1

is the average annual coupon rate based on a $100 price assumptions? I assumed the coupon YIELD is based on the beginning year bond price already and thus no need for adjustment. Seems that the answer here sees it different. The examples in the books all have beginning bond prices at $100 which is not helpful…

Exhibit 3

Selected Information for Calculation of Expected Return for Portfolio C

Investment horizon (years) 1 Average annual coupon rate for portfolio 2.09% Average beginning bond price for portfolio 101.01 Average ending bond price for portfolio (assuming roll-down and stable yield curve) 102.61 Expected effective duration for portfolio (at end of one year) 5.172 Expected convexity for portfolio (at end of one year) 0.799 Expected change in government bond yield curve –0.25%

Q. Based on the information provided in Exhibit 3, the expected return for Portfolio C is closest to:

  1. 4.70%.
  2. 3.65%.
  3. 4.95%.
    Solution

C is correct. The correct answer is 4.95%. Calculations are shown in the table below.

Yield income 2.07% Roll-down return 1.58% Total rolling yield 3.65% Expected price change based on yield view 1.29% Total expected return 4.95%

Yield income = 2.09/101.01 = 2.07%.

Roll-down return = 102.61/101.01 − 1 = 1.58%.

Total rolling yield = 2.07 + 1.58 = 3.65%.

Expected price change based on yield view = (−MD × ΔYield) + [½ × Convexity × (ΔYield)2] = (−5.172 × –0.0025) + [0.5 × 0.799 × (−0.0025)2] = 1.29%.

Total expected return = 3.65% + 1.29% = 4.95%.

#2

The answer seems alright. Are your asking if you calculate the yield income based on 100 price or the market value of the bond at the beginning of the period? If so, the second one is correct (as in the solution of your problem)

#3

I guess I’m thrown off by the % sign (Average annual coupon rate for portfolio = 2.09 % and not $ )

if the text were to state Average annual coupon = $2.09 then the yield income math would be clear. However, given its stated as % wouldn’t that already imply the yield income.

Effectively if the annual coupon rate as % the actual paid coupon for a $101.01 (beginning period) bond would be $2.11

#4

I agree if they use % it can seem ambiguous, and if they use $ it’s very clear. My advice is to assume the % is based on par, then you have to recalculate based on current price, since they want us to know we need to use current price and not par in the calculation.

#5

Sorry guys, I thought the discussion was about how to calculate the income yield. The coupon payment is in fact always coupon% * par (there are special cases, for instance inflation-linked bonds, where you dont use 100, but i dont think this will be covered on the exam).

#6

ok, great thank you guys!